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## Tuesday, 23 August 2022

IGNOU BCA fifth semester BCS 054 term-end exam notes, upcoming guess papers, important questions with solutions download. Success 90% in exam. IGNOU BCA BCS-054 term-end exam notes, upcoming guess papers, important questions with solutions download. IGNOU BCA/MCA all semester new revised (1st semester, 2nd semester, 3rd semester, 4th semester, 5th semester and 6th semester) solved assignments, term-end exam notes, study materials, important questions, books/blocks (June-December) free download.

IGNOU BCA BCS-054 5th semester Term-End Examination (COMPUTER ORIENTED NUMERICAL TECHNIQUES) books/block, term-end exam notes, upcoming guess paper, important questions, study materials, previous year papers with solutions.
 Chapter Topic with Solutions (90% success in exam) 1. Computer Arithmetic 2. Solution of Linear Algebraic Equation 3. Solution of Non-Linear Equations 4. Operators 5. Interpolation with Equal Intervals 6. Interpolations with Un-Equal Intervals 7. Numerical Differentiation 8. Numerical Integration 9. Numerical Integration 10. Old/Previous question papers with solutions (June 2014 to June 2017) 11. Guess Questions (Very Important for 90% Success in exam)
Notes-1

1. Using an 8-decimal digit floating point representation (4 digits for mantissa, 2 for exponent and one each for sign of exponent and sign for mantissa), represent the following numbers in normalised floating point form (using chopping, if required) :
(i) 87426
(ii) - 94.27
(iii)- 0.000346

2. For the following two floating point numbers

3. Find the product of x 1 and x2 given in Q. No. 2 above.

4. What is underflow ? Explain it with an example of multiplication in which underflow occurs.

5.What is overflow ? Explain it with an example.

6. Write the following system of linear equations in matrix form :
6x + 8y = 10
- 5x + 3y = 11

7. Show one iteration of solving the following system of linear equations using any iterative method. You may assume x = y= 0 as initial estimate.
-8x+ 7y= 15
5x - 2y=-7

8. Find an interval in which the following equation has a root :
4x2 - 4x - 3 = 0

9. Give one example of each of (i) algebraic equation (ii) transcendental equation.

10. Write the formula used in Newton-Raphson method for finding root of an equation.

11. Write the expressions, which are obtained by applying each of the operators to f(x), for some h :
(i) ∆ (ii) ∇ (iii) 𝛅 (iv) (v) E

12. Write  and 𝛅 in terms of E.    OR  Write  and 𝛍 in terms of E.

13. State the following two formula for (equal interval) interpolation :
(i) Newton's Backward Difference Formula
(ii) Newton's Forward Difference Formula
(iii) Stirling's formula

14. Construct a difference table for the following data :
x    1  2 3   4
f(x) 2 9 28 65

15. From the Newton's Forward Difference Formula asked in Q. No. 13 (ii) above,derive the formula for finding derivative of a function at X0.

16. State Simpson's (1/3) rule OR State Trapezoidal rule for finding the

17. Explain each of the following concepts with a suitable example :
(i) Initial Value Problem
(ii) Degree and order of a differential equation
OR
(i) Boundary Value Problem.
(ii) Order of a differential equation.

18. Let min. and max. represent respectively minimum and maximum positive real numbers epresentable by some floating point number system. Can every real number between max. and min. be representable by such a number system ? Explain the reason for your answer.

19. For each of the following numbers, find the floating point representation, if possible normalized, using chopping, if required. The format is 8-digit as is mentioned in Q. No. 1 above :
(i) 3/11
(ii) 74.0365
Further, find the absolute error, if any, in each case

20. Explain, with suitable examples, the advantages of using Normalized form for representing numbers.

21. Solve the following system of linear equations using Gaussian elimination method and comment on the nature of solution.
12x1 + 18x2 - 5x3 = 25
3x1 - 5x2 + 7x3 = 05
9x1 + 23x2 - 12x3 = 20

22. Find a 4÷b (a divided by b) for the floating point numbers :

23. Find the Taylor's series for X-1 at a = 1.

24. Obtain the smallest positive root of the equation x 3 - 5x + 1= 0, by using three iterations of bisection method.

25. Solve the following system of linear equations with partial pivoting condensation. Gaussian elimination method.

26. Give formula for next approximation of values of x1 , x2 and x3 using Gauss-Seidel method for solving a system of linear equations :

27. Describe relative merits of each of direct methods and iterative methods of solving system of linear equations, over each other.

28. What are the advantages of Direct methods over Iterative methods for solving a system of linear equations ?

29. Compute the difference table and mark the forward differences for x = 5.
x    f(x)
1    4
2    7
3   12
4   19
5   28

30. The population of a city in a census taken once in 10 years is given below in thousands.Estimate the value in 1965.
Year 1961 1971 1981 1991 2001 2011
Population 35 42 58 84 120 165

31. Find Newton's backward difference form of interpolating polynomial for the data :
x   4   6   8   10
f (x ) 19 40 83 155
Hence evaluate f (9).

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